(CNSNews.com) – The Obama administration’s response to the Sept. 11 attack on a U.S. consulate in Libya was aimed at reinforcing its storyline regarding successes against terrorism – an echo of its predecessor’s much-criticized premature claims concerning Iraq, according to senior Republican lawmakers.

Rep. Darrell Issa (R-Calif.), chairman of the House Oversight and Government Reform Committee, and Sen. Lindsey Graham (R-S.C.), a member of the Senate Armed Services Committee, both drew the Iraq comparison during television interviews on Sunday.

Following the attack on the consulate in Benghazi – which killed U.S. ambassador Chris Stevens and three other Americans – administration officials blamed the incident on protests over an online anti-Islam video. Only later did they concede it was a terrorist attack, with a likely al-Qaeda link.

Speaking on CBS’ “Face the Nation,” Graham said he believed the administration was aware within 24 hours of the attack that it was carried out by terrorists – not by Muslims protesting the video.

“They’re trying to sell a narrative, quite frankly, that the Mideast -- the wars are receding and al Qaeda’s been dismantled,” he charged. “I think they have been misleading us, but it finally caught up with them.”

President Bush visited the aircraft carrier USS Abraham Lincoln on May 1, 2003, to declare that all major combat operations in Iraq were over. (AP Photo/J. Scott Applewhite)

Graham compared the situation with the previous Republican administration’s handling of the situation in Iraq, following the March 2003 U.S.-led invasion to topple Saddam Hussein.

“I went to Iraq in 2004 and everybody told me things are going fine,” he recalled. “Iraq was falling apart, and you couldn’t get the truth from the Bush administration.”

Now, Graham said, “the Mideast is falling apart, and they’re trying to spin what happened in Libya because the truth of the matter is al-Qaeda is alive and well and counter-attacking.”

“When something goes bad, they deny, they deceive, and they delay. And the truth is we’re not safer. Al-Qaeda is alive – [Osama] bin Laden may be dead, al-Qaeda is alive and they’re counter-attacking throughout the entire region. And the truth is that the foreign policy choices of President Obama is allowing the region to come unraveled.”

Speaking on the same program, Issa, whose committee is holding hearings into the Benghazi affair with a particular focus on security failures, also made an Iraq comparison.

“We’re going through a ‘mission accomplished’ moment,” he said, referring to President Bush’s announcement on May 1, 2003 that all major combat operations in Iraq were over.

That declaration, less than two months after the war began, was soon shown to have been hasty, and critics – including media commentators – ridiculed the administration over it for years. Shortly before the end of his second term Bush acknowledged it was a mistake.

Issa suggested that the Obama administration was similarly jumping the gun with regard to the mission against al-Qaeda.

“This is not very Republican if you will, but when President George W. Bush went aboard an aircraft carrier and said, ‘mission accomplished,’ I listened – rightfully so – to people saying, ‘look, but there’s still problems, and they’re still dying,’ and quite frankly, things got worse in many ways after that famous statement.

“We’re going through a ‘mission accomplished’ moment. Eleven years after September 11th, Americans were attacked on September 11th [2012] by terrorists who preplanned to kill Americans,” he said.

“That happened, and we can’t be in denial. Particularly, when there are – there are [diplomatic] compounds all over the Middle East that need to be legitimately protected at a level that security professionals ask for it.”

Issa wants U.S. Ambassador to the United Nations Susan Rice to testify before his committee at a future hearing on the attack in Libya.

On Sept. 16, five days after the attack, Rice told a series of Sunday talk shows that, according to the best information available at the time, the incident was a “spontaneous reaction” to an online video clip denigrating Mohammed, rather than an unrelated terrorist attack.

Since then Rice and other administration officials have defended her comments, saying they were based on intelligence assessments at the time.

Just two days before Rice did the talk show round, however, the State Department informed reporters that it would answer no more questions on the Benghazi attack “until the Justice Department is ready to talk about the investigation.” Rice went on air to promote the video theory despite that declared decision, adding to Republican suspicions that the administration was trying to spin the events for political ends.

The ranking Democrat on the House Oversight Committee, Rep. Elijah Cummings (D-Md.), who also appeared on “Face the Nation,” voiced concern that the Benghazi attack was being “treated like a political football.”

Having listened to the Graham and Issa interviews, he said, “this conspiracy stuff is kind of ridiculous, to be honest with you. And I'm kind of surprised that they’ve gone to these lengths, but you know, that’s what they do.”

Cummings noted that investigations by the FBI and a State Department-appointed accountability review board were underway, “and we will get the answers.”

“But the way we’re doing it, I think, is basically based on a campaign schedule, trying to give [Republican presidential candidate Mitt] Romney some talking points.”